2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b99b3eb0-9bca-42e3-bea9-3b0454a872db-04_374_1084_246_493}
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\caption{Figure 2}
\end{figure}
Figure 2 shows a fairground ride that consists of a chair of mass \(m\) attached to one end of a rigid arm of length \(\frac { 5 a } { 4 }\). The other end of the arm is freely hinged to the rim of a thin horizontal circular disc of radius \(a\). The disc rotates with constant angular speed \(\omega\) about a vertical axis through the centre of the disc. As the ride rotates the arm remains in a vertical plane through the centre of the disc. The arm makes a constant angle \(\theta\) with the vertical, where \(\tan \theta = \frac { 3 } { 4 }\)
The chair is modelled as a particle and the arm is modelled as a light rod.
- Find the tension in the arm in terms of \(m\) and \(g\)
- Find \(\omega\) in terms of \(a\) and \(g\)